On the estimation of sound produced by complex fluid–structure interactions, with application to a vortex interacting with a shrouded rotor

1991 ◽  
Vol 433 (1889) ◽  
pp. 573-598 ◽  
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Leading Edge ◽  
Surface Forces ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Frequency Sound ◽  
Complex Fluid ◽  
Shrouded Rotor

An approximate analytical method is described for determining the sound produced by a class of complex fluid-structure interactions in low Mach number flows. This can be used to model noise sources in practical systems, and to check the accuracy of predictions based on time accurate numerical solutions of the Navier-Stokes equations. The dominant acoustic sources are dipoles whose strengths are dependent on the unsteady surface forces, and are expressed in terms of fluid velocity and vorticity, and a set of harmonic functions determined by the shapes of the structural elements interacting with the flow. (The theory of surface forces for arbitrary motion of a rigid body in viscous, incompressible flow in the presence of a fixed system of boundaries is discussed in an appendix.) These elements can influence both the generation and propagation of sound, and are frequently sources of new vorticity shed into wakes. The procedure is illustrated by application to a model problem in which sound is generated by a vortex interacting with a shrouded rotor in a duct. High-frequency sound is generated when the vortex is draw n into the rotor disc and ‘chopped’ by the blades. Sound is also produced through indirect blade-vortex interactions which, in this case, occur as a result of unsteady blade loadings produced when the core of the vortex is close to the leading edge of the shroud. This is relatively low-frequency sound and is the only component of blade-vortex interaction noise when the vortex is convected through the gap between the shroud and wall of the duct.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

scholarly journals A natural element updated Lagrangian approach for modelling fluid structure interactions

2007 ◽  
pp. 323-336
Author(s):  
Andrés Galavís ◽  
David González ◽  
Elias Cueto ◽  
Francisco Chinesta ◽  
Manuel Doblaré
Keyword(s):  
Stokes Equations ◽  
Theoretical Description ◽  
Navier Stokes ◽  
Fluid Structure Interactions ◽  
Navier Stokes Equations ◽  
Fluid Structure ◽  
Lagrangian Framework ◽  
Natural Element ◽  
Updated Lagrangian Approach ◽  
Updated Lagrangian

In this paper we present a novel methodology for the numerical simulation of fluid structure interactions in the presence of free surfaces. It is based on the use of the Natural Element Method (NEM) in an updated Lagrangian framework, together with the integration of the Navier-Stokes equations by employing a Galerkin-characteristics formulation. Tracking of the free-surface is made by employing shape constructors, in particular α- shapes. A theoretical description of the method is made and also some examples of the performance of the technique are included.

scholarly journals Parallel time-stepping for fluid-structure interactions

2021 ◽  
Author(s):  
Thomas Richter ◽  
Nils Margenberg
Keyword(s):  
Stokes Equations ◽  
Numerical Test ◽  
Time Integration ◽  
Navier Stokes ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Solution Approach ◽  
Time Stepping ◽  
Parallel Time ◽  
Nicolson Scheme

We present a parallel time-stepping method for fluid-structure   interactions. The interaction between the incompressible   Navier-Stokes equations and a hyperelastic solid is formulated in a   fully monolithic framework. Discretization in space is based on   equal order finite element for all variables and a variant of the   Crank-Nicolson scheme is used as second order time integrator. To   accelerate the solution of the systems, we analyze a parallel-in   time method. For different numerical test cases in 2d and in 3d we   present the efficiency of the resulting solution approach. We also   discuss some challenges and limitations that are connected   to the special structure of fluid-structure interaction problem.   In particular, we will investigate stability and dissipation     effects of the time integration and their influence on the     convergence of the Parareal method. It turns out that especially     processes based on an internal dynamics (e.g. driven by the vortex     street around an elastic obstacle) cause great     difficulties. Configurations however, which are driven by     oscillatory problem data, are well-suited for parallel time     stepping and allow for substantial speedups.

Space-time finite element computation of complex fluid-structure interactions

2010 ◽  
Vol 64 (10-12) ◽  
pp. 1201-1218 ◽  
Author(s):  
Tayfun E. Tezduyar ◽  
Kenji Takizawa ◽  
Creighton Moorman ◽  
Samuel Wright ◽  
Jason Christopher
Keyword(s):  
Finite Element ◽  
Space Time ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Element Computation ◽  
Complex Fluid ◽  
Finite Element Computation

A Numerical Study of Cavitation Induced Vibration

2010 ◽  
Author(s):  
M. Benaouicha ◽  
J. A. Astolfi ◽  
A. Ducoin ◽  
S. Frikha ◽  
O. Coutier-Delgosha
Keyword(s):  
Weak Coupling ◽  
Numerical Study ◽  
Plastic Material ◽  
Fluid Model ◽  
Leading Edge ◽  
Elastic Structure ◽  
Naval Academy ◽  
Fluid Structure ◽  
Complex Fluid ◽  
Coupling Algorithm

The present work deals with an original study of the dynamics of an elastic structure immerged in an unsteady partial cavitating flow. The latter corresponds to the case of a leading edge attached cavity that exhibits periodical oscillations. The elastic structure is a cantilevered rectangular hydrofoil made of polyacetal plastic material (E = 3GPa). The computational fluid dynamics is based on a 2D unsteady single fluid model of cavitation with a barotropic law and a k – ε – RNG modified turbulent model. The computational structure dynamics is carried out using a 3D finite element code. The fluid structure coupling is based on a chained weak coupling algorithm for which the 2D unsteady local fluid loading is computed on a rigid hydrofoil, then interpolated on the 3D deformable hydrofoil to compute the structural dynamics. The results are compared to the experiment ones carried out in the hydrodynamic tunnel of the research institute at the French Naval Academy for flow conditions close to the numerical ones. It is shown that in spite of a weak coupling algorithm, the forced vibration due to the periodical behaviour of the unsteady partial cavity is rather well predicted by the computation and compared favourably with the experiments. However, the experiments reveal that cavitation influences the natural modal response of the elastic structure in a more complex fluid structure interaction process.

Effect of a Lipid Pool on Stress/Strain Distributions in Stenotic Arteries: 3-D Fluid-Structure Interactions (FSI) Models

2004 ◽  
Vol 126 (3) ◽  
pp. 363-370 ◽  
Author(s):  
Dalin Tang ◽  
Chun Yang ◽  
Shunichi Kobayashi ◽  
David N. Ku
Keyword(s):  
Stokes Equations ◽  
Plaque Rupture ◽  
Strain Analysis ◽  
Fluid Structure Interactions ◽  
Stress Strain ◽  
Fluid Structure ◽  
Lipid Pool ◽  
Stenosis Severity ◽  
Stenotic Arteries

Nonlinear 3-D models with fluid-structure interactions (FSI) based on in vitro experiments are introduced and solved by ADINA to perform flow and stress/strain analysis for stenotic arteries with lipid cores. Navier-Stokes equations are used as the governing equations for the fluid. Hyperelastic Mooney-Rivlin models are used for both the arteries and lipid cores. Our results indicate that critical plaque stress/strain conditions are affected considerably by stenosis severity, eccentricity, lipid pool size, shape and position, plaque cap thickness, axial stretch, pressure, and fluid-structure interactions, and may be used for possible plaque rupture predictions.

Transient Cavitation in Fluid-Structure Interactions

1981 ◽  
Vol 103 (4) ◽  
pp. 345-351 ◽  
Author(s):  
C. A. Kot ◽  
B. J. Hsieh ◽  
C. K. Youngdahl ◽  
R. A. Valentin
Keyword(s):  
Essential Feature ◽  
Fluid Velocity ◽  
Structural Response ◽  
Computational Time ◽  
Fluid Structure Interactions ◽  
Time Step ◽  
Fluid Structure ◽  
Column Separation ◽  
Fluid Transient ◽  
Separation Model

A generalized column separation model is extended to predict transient cavitation associated with fluid-structure interactions. The essential feature of the combined fluid-structure interaction calculations is the coupling between the fluid transient, which is computed one dimensionally, and the structural response which can be multidimensional. Proper coupling is achieved by defining an average, one-dimensional, structural velocity and by assuming a spatially uniform pressure loading of the structure. This procedure is found to be effective even for very complex finite element structural models for which the required computational time step is orders of magnitude smaller than that for the fluid transient. Computational examples and comparison with experimental data show that neglecting cavitation and setting the fluid velocity at all times equal to that of the structural boundary leads to unreal negative pressure predictions. On the other hand a properly coupled column separation model reproduces the important features of fluid-structure interactions, converges rapidly, and gives reasonable fluid and structural response predictions.

Receptivity to surface roughness near a swept leading edge

1999 ◽  
Vol 380 ◽  
pp. 141-168 ◽  
Author(s):  
S. SCOTT COLLIS ◽  
SANJIVA K. LELE
Keyword(s):  
Surface Roughness ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Convex Surface ◽  
Cross Flow ◽  
Leading Edge ◽  
Surface Curvature ◽  
Parallel Flow ◽  
Navier Stokes ◽  
Swept Wing

The formation of stationary cross flow vortices in a three-dimensional boundary layer due to surface roughness located near the leading edge of a swept wing is investigated using numerical solutions of the compressible Navier–Stokes equations. The numerical solutions are used to evaluate the accuracy of theoretical receptivity predictions which are based on the parallel-flow approximation. By reformulating the receptivity theory to include the effect of surface curvature, it is shown that convex surface curvature enhances receptivity. Comparisons of the parallel-flow predictions with Navier–Stokes solutions demonstrate that non-parallel effects strongly reduce the initial amplitude of stationary cross flow vortices. The curvature and non-parallel effects tend to counteract one another; but, for the cases considered here, the non-parallel effect dominates leading to significant over-prediction of receptivity by parallel-flow receptivity theory. We conclude from these results that receptivity theories must account for non-parallel effects in order to accurately predict the amplitude of stationary crossflow instability waves near the leading edge of a swept wing.

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